Show that \sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{ \sin A}{1+\cos A}

ICSE Class X Math 2013 Solved Paper - Question 25

Question : 25 of 46

Marks: +1, -0

Show that

√{\;{1-\cos A}/{1+\cos A}}=\;{ \sin \;A}/{1+\cos A}

Solution:

\;\text " L.H.S. "\;=√{\;{1-\cos A}/{1+\cos A}}

Multiplying by

{√{1+\cos A}}

in numerator and denominator

\;=√{\;{1-\cos A}/{1+\cos A}} × √{\;{1+\cos A}/{1+\cos A}}

\;=√{\;{(1-\cos A)(1+\cos A)}/{(1+\cos A)(1+\cos A)}}

\;=√{\;{1-\cos ^2 A}/{(1+\cos A)^2}}=√{\;{ sin \;^2 A}/{(1+\cos A)^2}}

\;=\;{ sin \;A}/{1+\cos A}=\;\text " R.H.S. "\;

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